In a game of very few chances, both sets of defences were on top as Churchill Brothers moved two points clear of rock-bottom Rangdajied United while East Bengal have now dropped 17 points after just 12 games.
Churchill started strongly with Anthony Wolfe going close twice in the opening 10 minutes. East Bengal goalkeeper Gurpreet Singh Sandhu had to be alert on both occasions to deny the Trinidad and Tobago International.
Gurpreet then did well to stop Balwant Singh's powerful shot from 25 yards as the visitors continued to create pressure in the East Bengal half.
Churchill Brothers custodian Lalit Thapa was kept busy from crosses but rarely threatened from open play.
Shylo Malswamtluanga tested Thapa from outside the box but East Bengal's best chance of the half fell to Edeh Chidi who couldn't find the target after being played through by Malswamtluanga.
Both sides made early changes in the second half as Saran Singh replaced Alesh Sawant for Churchill Brothers while Armando Colaco introduced Harmanjot Khabra in place of Abhishek Das. But it remained a tight contest with very few clear cut opportunities.
East Bengal dominated possession in the second period and most of the play was in Churchill's half in the final quarter of the game.
But the hosts rarely got behind the back four of Churchill Brothers. And when they did create openings, either the first touch or final ball let them down.
Malswamtluanga and Chidi had a couple of half chances but neither could seriously trouble Thapa, who was adjudged Man of the Match for his impressive handling and decision making while dealing with crosses.